Chapter 3 – Solving Linear Equations 3.1 – Solving Equations Using Addition and Subtraction

3.1 – Solving Equations Using Addition and Subtraction Today we will be learning about: Solving linear equations using addition and subtraction Using linear equations to solve real-life problems

3.1 – Solving Equations Using Addition and Subtraction You and a friend are walking down Main Street and you find $10. You put it in your pocket with the rest of your money. At King’s later that day, you go to checkout and see that you have $28. How much money did you have before you found the $10?

3.1 – Solving Equations Using Addition and Subtraction When solving equations, our goal is to get the variable by itself. We need to get the variable on one side of the equal sign. We do this by adding and subtracting numbers from BOTH SIDES of the equation to keep the equation balanced. These are called EQUIVALENT EQUATIONS To get the variable by itself, we do the INVERSE OPERATION Operations that undo each other

3.1 – Solving Equations Using Addition and Subtraction EQUIVALENT EQUATIONS Adding the same number to each side ORIGINAL: x – 3 = 5 Add 3 to both sides EQUIVALENT: x = 8 Subtracting the same number from each side ORIGINAL: x + 6 = 10 Subtract 6 from both sides EQUIVALENT: x = 4

3.1 – Solving Equations Using Addition and Subtraction EQUIVALENT EQUATIONS Simplifying one or both sides ORIGINAL: x = 8 – 3 EQUIVALENT: x = 5 Interchange the sides ORGINAL: 7 = x EQUIVALENT: x = 7

3.1 – Solving Equations Using Addition and Subtraction Example 1 Solve the following equations: x – 9 = -17 -11 = n – (-2) 5 + x = -3

3.1 – Solving Equations Using Addition and Subtraction Example 2 The normal high temperature in January in Oley, Pennsylvania is 36°F and the normal low is 17°F. How many degrees apart are the high and low temperatures?

3.1 – Solving Equations Using Addition and Subtraction You have x dollars and your friends repays you the $7 he owes you. You now have $9. How much did you originally have? The temperature was x °F. It fell 2°F and is now 7°F. What was the original temperature? A 9 foot post extends x feet below the ground and 7 feet above ground. What is the length x buried below the ground? Example 3 Match the real-life problem with the equation. x + 7 = 9 x – 2 = 7 9 – x = 7

3.1 – Solving Equations Using Addition and Subtraction HOMEWORK Page 135 #22 – 40 even, 45 – 49